Journal of Hydrology xxx (2013) xxx–xxx
Contents lists available at SciVerse ScienceDirect
Journal of Hydrology
journal homepage: www.elsevier.com/locate/jhydrol
Five centuries of Upper Indus River flow from tree rings
Edward R. Cook a,⇑, Jonathan G. Palmer b,c, Moinuddin Ahmed d, Connie A. Woodhouse e, Pavla Fenwick c,
Muhammad Usama Zafar d, Muhammad Wahab d, Nasrullah Khan d
a
Tree Ring Laboratory, Lamont-Doherty Earth Observatory, Columbia University, Route 9W, Palisades, NY 10964, USA
Climate Change Research Centre (CCRC), School of Biological, Earth and Environmental Sciences, The University of New South Wales, Sydney 2052, NSW, Australia
c
Gondwana Tree-ring Laboratory, P.O. Box 14, Little River, Canterbury 7546, New Zealand
d
Botany Department, Federal Urdu University of Arts Science and Technology, Gulshan-e Iqbal, Karachi, Sind 75300, Pakistan
e
School Geography and Development, University of Arizona, P.O. Box 210076, Tucson, AZ 85721, USA
b
a r t i c l e
i n f o
Article history:
Received 29 October 2012
Received in revised form 1 February 2013
Accepted 2 February 2013
Available online xxxx
This manuscript was handled by
Konstantine P. Georgakakos, Editor-in-Chief
Keywords:
Dendroclimatology
Upper Indus Basin discharge
Streamflow reconstruction from tree rings
Semi-parametric prediction intervals
Discharge regime shifts
s u m m a r y
Water wars are a prospect in coming years as nations struggle with the effects of climate change, growing
water demand, and declining resources. The Indus River supplies water to the world’s largest contiguous
irrigation system generating 90% of the food production in Pakistan as well as 13 gigawatts of hydroelectricity. Because any gap between water supply and demand has major and far-reaching ramifications, an
understanding of natural flow variability is vital – especially when only 47 years of instrumental record
is available. A network of tree-ring sites from the Upper Indus Basin (UIB) was used to reconstruct river discharge levels covering the period AD 1452–2008. Novel methods tree-ring detrending based on the ‘signal
free’ method and estimation of reconstruction uncertainty based on the ‘maximum entropy bootstrap’ are
used. This 557-year record displays strong inter-decadal fluctuations that could not have been deduced
from the short gauged record. Recent discharge levels are high but not statistically unprecedented and
are likely to be associated with increased meltwater from unusually heavy prior winter snowfall. A period
of prolonged below-average discharge is indicated during AD 1572–1683. This unprecedented low-flow
period may have been a time of persistently below-average winter snowfall and provides a warning for
future water resource planning. Our reconstruction thus helps fill the hydrological information vacuum
for modeling the Hindu Kush–Karakoram–Himalayan region and is useful for planning future development
of UIB water resources in an effort to close Pakistan’s ‘‘water gap’’. Finally, the river discharge reconstruction
provides the basis for comparing past, present, and future hydrologic changes, which will be crucial for
detection and attribution of hydroclimate change in the Upper Indus Basin.
! 2013 Elsevier B.V. All rights reserved.
1. Introduction
Pakistan is located in an extremely arid region, with an average
rainfall of less than 240 mm a year making it ‘‘one of the world’s
most water-stressed countries’’ (World Bank, 2005). The rapidly
growing population and economy are heavily dependent on water
from the Indus River Basin to supply the largest contiguous irrigation system in the world that in turn yields 90% of the food production in Pakistan (Qureshi, 2011). The overall basin consists of six
main rivers (the Indus, Jhelum, Chenab, Ravi, Sutlej, and Kabul)
originating from glaciers in the Karakoram and western Himalaya.
Collectively these rivers provide irrigation water to more than
16 million hectares of agricultural land and generate up to 13 gigawatts of electricity through hydropower plants in Pakistan, India,
and Afghanistan (ICIMOD, 2010). Thus, as the Indus River Basin
goes, so goes Pakistan.
⇑ Corresponding author. Tel.: +1 845 365 8618.
E-mail address: [email protected] (E.R. Cook).
The Indus River itself contributes about 43% of the total annual
flow of the basin, and 72% of that discharge comes from the
‘‘Northern Areas’’ of Pakistan (Ahmed and Joyia, 2003). The latter
constitutes the Upper Indus Basin (UIB), which provides water
for the storage lake behind Tarbela Dam as the river emerges from
the mountains. This reservoir was primarily designed for irrigation
and provides canal irrigation water for a substantial fraction of
Pakistan’s agricultural production. It also has an installed hydroelectric capacity of 3478 MW, which amounts to 49% of Pakistan’s
total hydroelectric power capacity (http://environmentdefencer.wordpress.com/tag/tarbela-dam/). So without question, adequate UIB discharge into Tarbela Reservoir is crucial to the
economic and social wellbeing of the people of Pakistan.
The potential vulnerability of Pakistan to changes in UIB
streamflow is indicated by recent events [or conditions]. In March
2012, the water level of Tarbela Reservoir dropped to ‘‘dead level’’
(http://tribune.com.pk/story/346909/water-in-tarbela-dam-touchesdead-level/), the point at which useful water yield is zero, and
as of August 2012, the water level was still below normal due to
0022-1694/$ - see front matter ! 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.jhydrol.2013.02.004
Please cite this article in press as: Cook, E.R., et al. Five centuries of Upper Indus River flow from tree rings. J. Hydrol. (2013), http://dx.doi.org/10.1016/
j.jhydrol.2013.02.004
2
E.R. Cook et al. / Journal of Hydrology xxx (2013) xxx–xxx
insufficient inflow of snow and glacier meltwater into the reservoir
because of below-average prior winter snows in the mountains
(http://www.geo.tv/GeoDetail.aspx?ID=63047). ‘‘Dead level’’ may
occur from time to time due to the normal seasonal drawdown
of water based on irrigation and hydropower demands, but the
failure of the UIB to refill the reservoir to normal levels so late in
the principal runoff season is alarming. This is an example of the
‘‘water gap’’ between supply and demand that is increasingly facing Pakistan now (World Bank, 2005).
Thus, an obvious question is how reliable is the UIB for providing enough discharge to support both irrigation and hydropower
generation needs? This is an open question because so little is
known about the long-term properties of the UIB hydrologic regime and its principal contributors, snow and glacier meltwater.
The most representative record of total discharge into Tarbela Reservoir is upstream at Besham and it only begins in 1969 (Archer,
2003), a short 44-year long record that is inadequate for modeling
the long-term properties of river discharge (Rodriguez-Iturbe,
1969). In addition, the short streamflow records available provide
no context for assessing recent trends and shifts in flow volume.
These problems echo the more general concern voiced by Pellicciotti et al. (2012) over the ‘‘striking scarcity of hydro-meteorological and glaciological data’’ for hydrological modeling of the
Hindu Kush–Karakoram–Himalayan region.
We address part of this information need through the reconstruction of UIB runoff from long, climatically sensitive, annual
tree-ring chronologies in northern Pakistan. Specifically, we present a calibrated and validated reconstruction of runoff for the peak
May–September discharge season for the UIB. This reconstruction
extends back to 1452 C.E. As such, it provides a far more complete
record of discharge variability and change over a range of timescales from annual to centennial and over a range of climate states
from the early stages of the ‘‘Little Ice Age’’ (Gove, 1988) to the current epoch of anthropogenic climate change in the 20th and 21st
centuries, referred to by some as the ‘‘Anthropocene’’ (Crutzen,
2002). River flow reconstructions of the kind presented here (cf.,
Stockton and Jacoby, 1976; Cook and Jacoby, 1983; Cleaveland,
1999; Woodhouse et al., 2006; Meko et al., 2007) have greatly increased our understanding of how discharge has varied over time
in ways not possible from the relatively short gauged records that
are typically available.
2. Upper Indus Basin discharge at Partab Bridge
The UIB discharge record at Partab Bridge (34"430 N, 74"380 E;
elev. 1250 m; Fig. 1; Archer, 2003) was chosen for tree-ring reconstruction because it is the longest, most representative, discharge
record for the UIB. It represents 145,618 km2 or 87.7% of the
Fig. 1. Map of the Upper Indus Basin in Pakistan showing the Indus River and its main tributaries in blue and the locations of the tree-ring chronologies (open red triangles)
used for reconstructing May–September discharge at Partab Bridge (inverted filled black triangle). The tree species used for reconstruction are Abies pindrow, Juniperus excelsa,
Cedrus deodara, Picea smithiana, Pinus gerardiana, and Pinus wallichiana. The three sizes of open tree-ring triangles are scaled by correlation with discharge (small: 0.30–0.39,
medium: 0.40–0.49, large: P0.50). The more highly correlated tree rings tend to be closer to the Partab Bridge record. The filled black dots are the cities of Peshawar and
Islamabad. The map is courtesy of Paul J. Krusic and Generic Mapping Tools. (For interpretation of the references to colour in this figure legend, the reader is referred to the
web version of this article.)
Please cite this article in press as: Cook, E.R., et al. Five centuries of Upper Indus River flow from tree rings. J. Hydrol. (2013), http://dx.doi.org/10.1016/
j.jhydrol.2013.02.004
3
E.R. Cook et al. / Journal of Hydrology xxx (2013) xxx–xxx
Partab Bridge Discharge
Three-Gauge Estimates
2400
2200
2000
1800
1600
1400
1200
1960
(a) Indus River at Kachora (35"270 N, 75"250 E) for 1970–2008.
(b) Hunza River at Dainyor (35"560 N, 74"230 E) for 1966–2008
(missing: 2005, 2006, and 2007).
(c) Gilgit River at Gilgit (35"560 N, 74"180 E) for 1960–2008 (missing: July–December, 1999).
1970
1980
1990
2000
2010
Year
Monthly Hydrograph At Partab Bridge
8000
Discharge (m3s-1)
7000
6000
5000
May-Sep
discharge
totals 85%
of annual
discharge
4000
3000
2000
1000
0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month
5500
Mean May-Sep Discharge At Partab Bridge
5000
Discharge (m3s-1)
The sum of the mean annual flows for these gauges match the
pattern of discharge at Partab Bridge very well (r = 0.96) for the
years of overlap, 1970–1972 and 1980–1996, but with a systematic
offset in mean level due to relatively minor missing discharge from
other sources (142.6 m3 s!1 or 8% of mean annual flow). These results allowed us to proceed with updating the Partab Bridge
monthly record to 2008. To complete the record, Indus River at
Kachora monthly flows were first used to estimate the missing
6 months of data in 1999 for the Gilgit River record and the 3 years
of data missing for the Hunza River. The method for estimating
those missing data was based on the ratio method commonly used
for estimating missing precipitation data (Chow et al., 1988), in
which the missing value for a given year was estimated based on
the ratio of that year’s value to the average value for a gauge with
complete data, along with the average for the station with the
missing value. The final monthly sums of the three gauges were
then adjusted to match the Partab Bridge values for the 1980–
1996 years of overlap to account for offsets in mean level. The
resulting three-gauge sum matches the flow at Partab Bridge for
the years of overlap with a mean offset of only +0.2% (Fig. 2A).
The updated Partab Bridge record has a mean annual flow of
1798 m3 s!1 over it full period of record, which reflects 74% of
the mean annual discharge into Tarbela Reservoir as measured just
above it at Besham (1969–1997; no available data from 1998 to
2008). Since the two gauge records have a correlation of 0.82 over
their 1969–1997 common period, we expect the variability in
reconstructed flow at Partab Bridge to be broadly representative
of the full UIB.
The monthly hydrograph at Partab Bridge is shown in Fig. 2B as
a series of boxplots. It reveals the extreme seasonality of UIB flow
recorded at this gauging station, with 85% of the mean annual discharge concentrated in the May–September period and much reduced and much less variable discharge in the other months.
Thus, almost all UIB variability occurs during the warm season
months, and this contributes to most of the observed interannual
variability in discharge. Seasonal snow and glacier meltwater are
most important here because the mean elevation of the
176,775 km2 basin above Partab Bridge is 4656 m. This means
most of the cold-season precipitation falls as snow (Hewitt,
2005) and remains on the ground until temperatures raise above
freezing in the spring. Above 3500 m, snowcover in the UIB begins
disappearing in early spring and is largely gone by sometime in August (Winiger et al., 2005). But for the significantly greater area
being drained above Partab Bridge, this process would be delayed
in the way seen in the hydrograph. Immerzeel et al. (2009) estimated that up to 72% of all runoff in the UIB is from a combination
Mean Annual Discharge At Partab Bridge
2600
Discharge (m3s-1)
gauged basin area draining into Tarbela Reservoir at Besham (Alford, 2011; Sharif et al., 2012) and begins in 1962, making it
slightly longer than the Besham record. Monthly data for this
gauge was previously made available for study by the Pakistan
Water and Power Development Authority (WAPDA) for the years
1962–1996 (e.g., Archer, 2003). Subsequently, WAPDA provided
us with streamflow updates to 2008 for the Indus and its major
tributaries upstream from Partab Bridge, but not for Partab Bridge
itself. Fortunately, these post-1996 upstream updates allowed us
to usefully extend the Partab Bridge record to 2008 with a high degree of accuracy.
The specific monthly discharge records used for estimating Partab Bridge from 1997 to 2008 were:
4500
4000
3500
3000
2500
1960
1970
1980
Year
1990
2000
2010
Fig. 2. The Partab Bridge discharge record for the upper Indus River since 1962. To
be used, it required updating from 1997 to 2008 using the sum of three upstream
records at Kachora, Hunza, and Gilgit (A). See the text for details. The estimates
(red), adjusted upward for differences between the three-gauge sum and discharge
at Partab Bridge, produced a very good fit in the overlap period, which justifies
using those estimates as updates to 2008. The resulting monthly hydrograph (B)
calculated from the updated record at Partab Bridge shows that May–September
discharge accounts for 85% of the mean annual flow and almost all of its interannual
variability. The May–September average discharge record (C) was consequently
used for reconstruction. The red curve is a 50% LOWESS robust smooth that
highlights an apparent shift in average flow from 1987 to 1988. (For interpretation
of the references to colour in this figure legend, the reader is referred to the web
version of this article.)
of seasonal snow (40%) and glacier (32%) meltwater. Modeling
experiments by Immerzeel et al. (2010) suggested an even higher
(40%) glacier meltwater contribution. In contrast, Bookhagen and
Burbank (2010) estimated the annual snowmelt contribution could
Please cite this article in press as: Cook, E.R., et al. Five centuries of Upper Indus River flow from tree rings. J. Hydrol. (2013), http://dx.doi.org/10.1016/
j.jhydrol.2013.02.004
4
E.R. Cook et al. / Journal of Hydrology xxx (2013) xxx–xxx
be as high as 66% in the UIB, which is more in line with an even
higher estimate of 82% between late-spring snowcover area and
subsequent streamflow recorded at Besham from 1969 to 1973
(Rango et al., 1977). There is clearly much uncertainty concerning
the relative contributions of snow and glacier meltwater to UIB
discharge.
Based on the monthly hydrograph, May–September discharge
at Partab Bridge was chosen as the season to reconstruct because
it encompasses most of the annual discharge and almost all of its
interannual variability. Of equal importance, May–September
broadly matches the extended physiologically active season of
the trees used here for reconstruction. This discharge record is
shown in Fig. 2C. It has a correlation of 0.996 with the mean annual
series (Fig. 2A), with the same regime-like shift in discharge from
1987 to 1988. The step-like increase in river flow since 1988 could
be related to increased seasonal snowfall in the upper elevations,
which has a maximum accumulation between 5000 and 6000 m
(Hewitt, 2005), or perhaps increased glacier meltwater. At lower
elevations, Archer and Fowler (2004) reported an increase in winter precipitation from 1961 to 1999 at several locations in the
Karakoram range. A simple trend line fit to the discharge data from
1962 to 1999 also yields a positive trend (r = 0.33; p < 0.05), which
is consistent with the results of Archer and Fowler (2004). However, this trend is neither gradual nor homogeneous. Rather, it is
largely driven by the abrupt jump in discharge beginning in
1988. Immerzeel et al. (2009) later used MODIS satellite measurements to construct a seasonal snow cover record from 2000 to
2008 for the UIB, which post-dates the abrupt increase in discharge. In contrast to the previous results, they found evidence
for a decreasing trend in winter snow cover in two elevation zones
above 4700 m, with the highest zone above 5000 m having the
strongest negative trend. The robust LOWESS smooth (Fig. 2C) also
shows evidence for a weak negative trend in May–September discharge since 2000. Consistent with this suggestion, Shekhar et al.
(2010) likewise reported a weak negative trend in Karakoram
November–April snowfall since 1991/92. A similar weak trend is
evident in the discharge data from 1992 to 2008. Unfortunately,
none of these studies of winter precipitation change provide any
insights into the cause of the jump in streamflow from 1987 to
1988.
An abrupt increase in glacier meltwater has not been considered thus far as a contributor to the jump in May–September discharge increase since 1988. The consensus opinion is that the
glaciers of the Karakoram are reasonably stable (Hewitt, 2005;
Schmidt and Nusser, 2009; Armstrong, 2010; Bolch et al., 2012;
Gardelle et al., 2012), which implies that the glacier meltwater
contribution over the 1962–2008 period has probably not increased enough to explain the increase in discharge. In addition,
the Karakoram range has experienced a decreasing trend in
spring/summer temperatures since the 1960s (Fowler and Archer,
2006; Shekhar et al., 2010), which argues for an actual decrease in
glacier meltwater flux since 1988. In contrast, Immerzeel et al.
(2009) argued that the Karakoram have in fact warmed over the
past few decades. Paradoxically, their analyses are based on gridded temperature data based on some of the same station data used
by Fowler and Archer (2006). Why these apparent differences exist
is not clear.
Viewed in its entirety, observed May–September discharge at
Partab Bridge can be interpreted in different ways. One plausible
interpretation (akin to a null hypothesis here) is that warm-season
UIB discharge has been experiencing natural interdecadal variability since 1962 around a relatively stationary long-term mean of
3674 ± 77 m3 s!1 (±1 standard error). The data also allow for two
quite different alternate hypotheses: (1) that near-normal flow occurred from 1962 to 1987 (3470 ± 95 m3 s!1) followed by anomalously high flow from 1988 to 2008 (3926 ± 105 m3 s!1), or (2)
that anomalously low-flow occurred from 1962 to 1987 followed
by a return to essentially normal flow from 1988 to 2008. Either
way, a t-test of the difference between the two means (assuming
normality, independence, and unequal variances) is statistically
significant (p < 0.002), but the two alternate hypotheses are quite
different in their hydrological interpretations. With only 47 years
of UIB discharge data roughly split in half by the two putative regimes, it is impossible to say if either of these alternate hypotheses
is more plausible than the null hypothesis based on all the data.
The uncertainties in the statistical properties of such short hydrologic records are too large to provide useful estimates of long-term
flow characteristics for modeling and simulation (RodriguezIturbe, 1969). These limitations indicate why a multi-centennial
tree-ring reconstruction of UIB discharge would be so useful because it would put into long-term context the pattern of variability
observed in the short Partab Bridge discharge record and provide
improved estimates of its statistical properties at interdecadal
and longer time scales (cf. Woodhouse et al., 2006; Meko et al.,
2007).
3. The Upper Indus Basin tree-ring network
The high-elevation conifer forests of the UIB contain a diverse
mix of tree species that can be used for reconstructions of past climate. This potential was first demonstrated by Ahmed (1989) for
the Himalayan fir Abies pindrow and further documented by Esper
et al. (1995) through the detailed sampling and analysis of the juniper species Juniperus excelsa in and around the Hunza Valley region
of northern Pakistan. Other tree species available for sampling include Cedrus deodara, Pinus gerardiana, Pinus wallichiana and Picea
smithiana (Ahmed and Sarangezai, 1991; Ahmed and Naqvi,
2005; Ahmed et al., 2011). Given this potential, and support from
the Pakistan-U.S. Science and Technology Cooperation Program, a
concerted effort was made to develop a dense multi-species treering network for reconstructing UIB discharge. This effort resulted
in a network of 39 well-replicated annual tree-ring chronologies
(see Ahmed et al., 2011), all precisely dated following standard
dendrochronological cross-dating techniques (Stokes and Smiley,
1968). Of the 39 chronologies, 26 are new, including two located
in far eastern Afghanistan, while the remaining 13 (all J. excelsa)
are from earlier collections by Esper et al. (1995). Several species
in this network have trees with ages up to "700 years (C. deodara,
P. gerardiana, P. wallichiana and P. smithiana), but J. excelsa is the
longest lived with some trees exceeding 1000 years of age.
The raw ringwidth measurement data for each of the 39 sites
are annual records of radial tree growth measured in units of millimeters per year. As such they contain non-climatic growth trends
related to biological and geometrical constraints on radial growth.
These non-climatic trends are typically removed through curve fitting and detrending by a procedure called ‘tree-ring standardization’ (Fritts, 1976; Cook and Kairiukstis, 1990). Here, we use
detrending based on the relatively new ‘signal free’ (SF) method
(Melvin and Briffa, 2008), which is designed to enhance the preservation of common medium-frequency variance (timescales of decades to a century or more) in tree chronologies. Using the SF
method, ‘‘trend distortion’’ effects during the detrending phase of
tree-ring chronology development are eliminated. This problem
is caused by the influence of common persistent medium-frequency signals (e.g. increases in growth caused by climate) on
the fitting of the detrending curves. This common signal can bias
the removal of supposed ‘‘non-climate’’ variance, leading to distortion of the external forcing signal in tree-ring chronologies (Melvin
and Briffa, 2008). Trend distortion is most prevalent at the ends of
the chronologies, but can occur anywhere in a tree-ring series
when flexible curve fitting methods (e.g. smoothing splines; Cook
Please cite this article in press as: Cook, E.R., et al. Five centuries of Upper Indus River flow from tree rings. J. Hydrol. (2013), http://dx.doi.org/10.1016/
j.jhydrol.2013.02.004
E.R. Cook et al. / Journal of Hydrology xxx (2013) xxx–xxx
and Peters, 1981) are used. As such, the SF method can also correct
for lost common medium-frequency variance and mitigate the effects of the ‘segment length curse’ (Cook et al., 1995) on the preservation of variability in excess of the lengths of the tree-ring series
used in chronology development. We have performed SF standardization on all of our tree-ring chronologies used for reconstruction
of May–September discharge at Partab Bridge. In so doing, it is possible to evaluate the properties of UIB streamflow from interannual
to centennial timescales.
Intense environmental gradients are present in the Karakoram,
as indicated by Archer and Blenkinsop (2010), who found high heterogeneity between climate station data there. Correlations between the 28 site chronologies (ranging from 2450 to
3900 m.a.s.l.) were similarly investigated as a function of increasing separation distance between sites and species (Ahmed et al.,
2011). A similar decline in correlation with increasing distance
was consistently found both between sites of the same species
and between sites composed of different species. In some cases, a
much stronger correlation occurred between different species
growing at the same site than between different sites of the same
species, but separated by as little as 0.5 km. Such results highlight
the strong elevational gradients and highly variable slope aspects
present in the Karakoram. Even so, Ahmed et al. (2011) showed
through correlations between a subset of Karakoram tree rings
chronologies used here and gridded monthly temperature and precipitation data over the Karakoram region that there was a strong
common climate signal among the chronologies. In most cases, the
chronologies correlated positively with some or all of the Januaryto-May months of precipitation preceding the growing season and
negatively with some or all of the April-to-July months of temperature during the growing season. So it appears that seasonal snowfall is the primary source of soil moisture for subsequent tree
growth in the Karakoram, with summertime temperature affecting
radial growth through evapotranspiration demand during the photosynthetically active warm season.
Archer and Blenkinsop (2010) argued that a reconstruction of
hydroclimate from tree rings in the Karakoram was unlikely to
be successful because of intense environmental gradients there.
As we will show, this interpretation is unduly pessimistic. The
combination of a sufficiently dense and diverse multi-species
tree-ring network and a well-tested statistical method for dendroclimatic reconstruction have successfully produced a skillful reconstruction of May–September discharge for the Upper Indus River at
Partab Bridge covering the period 1452–2008.
4. The streamflow reconstruction method
For reconstruction of UIB discharge at Partab Bridge, we used a
principal components regression (PCR) approach that has been
used previously to reconstruct climate from tree rings (Cook
et al., 1999; 2004; Cook et al., 2010a, 2010b). This approach produces a ‘nested’ suite of reconstructions (cf. Meko, 1997; Cook
et al., 2002; Wilson et al., 2007) in which shorter tree-ring series
used as predictors are sequentially eliminated from the predictor
pool used in PCR until the pool is exhausted. Each of the nested
reconstructions is separated by at least 10 years. The full ‘nested’
reconstruction is then created by appending each subset-reconstruction extension back in time to the beginning of pre-existing
shorter reconstruction after appropriate scaling to recover lost variance due to regression in each reconstruction, thus producing the
longest possible reconstruction from the available tree-ring data.
The scaling is done to insure that no artificial variability due to differences in regression R2 from nest to nest is present in the full
nested reconstruction. The recovery of lost variance due to regression also provides for less biased comparisons of current with past
5
climate fluctuations, but at the cost of increased uncertainty in the
estimates (Ammann et al., 2010). Since changes in mean discharge
are of primary interest here, this tradeoff is considered acceptable.
In developing tree-ring based reconstructions, it is important to
assess model skill over the calibration period and over years that
have been withheld from the calibration for model validation. For
each nested subset model, a suite of calibration and validation statistics is produced., (e.g., Michaelsen, 1987; Meko, 1997; Cook
et al., 1999, 2004, 2010a, 2010b): CRSQ (calibration period coefficient of multiple determination or R2), CVRE (calibration period
reduction of error calculated by leave-one-out cross-validation),
VRSQ (validation period square of the Pearson correlation or r2),
VRE (validation period reduction of error) and VCE (validation period coefficient of efficiency). VRE and VCE differ from VRSQ in the
way that they use the calibration and validation period means,
respectively, as baselines for assessing model skill. When positive,
these statistics can all be interpreted as somewhat different
expressions of variance in common between the actual and estimated data. However, unlike CRSQ, which can never be negative,
CVRE, VRSQ (by retaining the negative sign of r after squaring),
VRE and VCE can also be negative, indicating that there is no skill
in the estimates. See Cook et al. (1999, 2004) for details. The difficulty in estimating the actual statistical significance of CVRE, VRE,
and VCE even when positive has always been a problem because no
theory-based tests of these statistics exist. This limitation has been
largely eliminated here through the novel use of the maximum entropy bootstrap (MEBoot; Vinod, 2006; Vinod and López-de-Lacalle, 2009) to estimate reconstruction uncertainties. In so doing, nonparametric uncertainties for all of the nested calibration and validation statistics naturally emerge from the reconstruction
procedure.
Besides reporting the calibration/validation statistics described
above, uncertainties on the estimates themselves are also provided
in the form of regression prediction intervals (Seber and Lee, 2003;
Olive, 2007) estimated as:
pffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Y^ f # t n!p;1!a=2 MSE ð1 þ hf Þ
ð1Þ
hf ¼ xTf ðX T XÞ!1 xf
ð2Þ
where Yf is the regression estimate, t is the 1!a/2 t-statistic with n–
p degrees of freedom, MSE is the mean square error of the fitted calibration model, and hf is the ‘‘leverage’’ from the hat-matrix of predictors for each year calculated as:
where X is the design matrix of predictors used for calibration and xf
is the vector of values used for prediction in year f. The primary difference from Eq. (1) implemented here is that the fixed t-statistic
(assume 90% 2-tailed limits) for scaling the uncertainties are replaced by the variable 5th and 95th quantiles (90% quantile limits)
from a suite of pseudo-reconstructions produced after applying MEBoot to both the predictor and predictand data prior to regression.
This includes any pre-processing of the original candidate tree-ring
chronologies up to the final regression model (e.g., prewhitening
and predictor variable screening; cf. Cook et al., 1999). So, except
for the selection of the original pool of candidate tree-ring predictors and the preprocessing that is used to create those annual
tree-ring chronologies, all steps in the regression modeling procedure are incorporated in the MEBoot procedure used here. Because
the fixed t-statistic has now been replaced by the variable nonparametric MEBoot 90% quantiles, but the overall regression-based
parametric form of Eq. (1) remains intact, we refer to our uncertainties as semi-parametric prediction intervals. See Olive (2007) for
alternative ways of modifying the calculation of prediction intervals
to make them more general.
The maximum entropy bootstrap is distinctly different from the
classical bootstrap (Efron, 1979) because it does not randomly
Please cite this article in press as: Cook, E.R., et al. Five centuries of Upper Indus River flow from tree rings. J. Hydrol. (2013), http://dx.doi.org/10.1016/
j.jhydrol.2013.02.004
6
E.R. Cook et al. / Journal of Hydrology xxx (2013) xxx–xxx
sample with replacement all of the available data, or in our case,
data across time. To do so would break up the temporal order of
the sequence, which is a defining property of the series. In contrast,
MEBoot preserves the overall shape (i.e., the temporal order) of the
data, which allows for direct estimates of uncertainty to be made
from the ensemble of MEBoot pseudo-reconstructions. MEBoot is
also unique in the way it preserves the persistence structure and
overall properties of any arbitrary stochastic process, including
those that are non-stationary and heteroscedastic. This can be difficult if not impossible to do using the moving block bootstrap (cf.
Wilks, 1997). In so doing, MEBoot satisfies both the ergodic theorem and central limit theorem (Vinod and López-de-Lacalle,
2009), which provides it with very nice asymptotic properties. Collectively, this guarantees that the overall stochastic properties of
the original time series used in regression are well preserved in
the ensemble of MEBoot pseudo-series. Thus, MEBoot adds a natural element of randomness to each pseudo-reconstruction, while
preserving the overall stochastic properties of the predictor–predictand data. In this sense MEBoot can be thought of as a perturbation method. See Vinod and López-de-Lacalle (2009) for details and
Vinod (2010) for a discussion on the use of MEBoot as a solution to
the spurious time series regression problem.
We applied MEBoot to both the tree-ring predictors and steamflow predictand data here. This explicitly admits that there is some
error on both sides of the regression model equation to consider,
but these errors are either unknown or very difficult to estimate
with much certainty. This makes the use of more formal ‘total least
squares’ methods (e.g., Hegerl et al., 2007) difficult to apply because the ratio of error variances of the predictors and predictand
is assumed known or at least estimated in a reasonably precise and
unbiased way. In lieu of explicitly estimating these weakly constrained error variances, we use MEBoot as a perturbation method
that imparts a reasonable level of random error to each series datum prior to regression modeling. This was done 300 times here (a
number sufficient for "90% intervals) to produce an empirical
probability density function of uncertainty for each year as a
replacement for the t-distribution. This non-parametric part of
the prediction interval equation allows the estimated uncertainties
to have variable coverage from year to year and to also be asymmetric as dictated by the data. Coupling these 90% quantile uncertainties with the MEBoot 95th quantile of MSE and hf (the upper
90% quantile limit) for each reconstruction nest completes the estimation of the 90% semi-parametric prediction intervals.
The original parametric form of the prediction intervals in Eq.
(1) has been preserved here, but it now estimates those intervals
in a more non-parametric, data-adaptive way. The leverage terms
can also used to identify those years that fall outside the range of
the calibration period data and thus behave as extrapolations
(Weisberg, 2005). In these cases, the prediction intervals are far
less reliable (Olive, 2007). Also, because 300 pseudo-reconstructions have been estimated now for generating the semi-parametric
prediction intervals, it follows that there are also 300 pseudo-estimates of the calibration and validation statistics described earlier
for generating their 90% uncertainty intervals, including those for
VRE and VCE for which there are no theory-based confidence intervals available to calculate.
5. Tree-ring reconstruction of upper Indus River discharge
The nested reconstruction of UIB May–September discharge
was produced using the PCR approach described above. It is based
on a 24 tree-ring chronology subset of the 39 available from the
UIB, using only those ending on or after 2005 in order to maintain
a common time interval with the Partab Bridge discharge record,
The 24 tree-ring chronologies begin anywhere from 1260 to 1738
and all end on or after 2005. However, the minimum acceptable
sample size for each annual mean tree-ring index value in each
chronology was set to five to eliminate the more weakly replicated
and least reliable inner portions of the chronologies. This resulted
in a change from 1260 to 1452 for the earliest start year and from
1738 to 1800 for the latest start year.
The calibration period chosen to develop the nested regression
models was 1975–2004 (30 years), with the 1962–1974 period
data (13 years) withheld for independent validation of the treering estimates (cf. Fritts, 1976; Snee, 1977; Picard and Berk,
1990). The validation period is relatively short, but this limitation
is compensated for in the following section by comparisons of
the reconstruction to fully independent tree-ring-based hydroclimatic records from the UIB. Each chronology was evaluated for correlation with May–September discharge for both year t and t + 1 (a
total of 48 candidate predictors) and only those chronologies that
correlated significantly (p < 0.10, 2-tailed) were retained as predictors in PCR (cf. Cook et al., 1999). This screening procedure reduced
the predictor set from 48 candidates to 15 actually used in PCR.
This included the retention of five tree species (A. pindrow, J. excelsa, C. deodara, P. smithiana, P. gerardiana, and P. wallichiana), with
all but two being positively correlated with discharge in year t.
The climate correlation results of Ahmed et al. (2011) suggest that
these positive correlations are related to a positive response to
winter–spring precipitation and the subsequent contribution of
seasonal snowmelt to discharge. The geographic distribution of
chronologies used, size-coded by strength of correlation with discharge, is shown in Fig. 1. It can be seen that the distribution of
sites covers a large geographic portion of the Upper Indus River Basin. The more highly correlated tree rings tend to be closer to the
Partab Bridge gauging station.
The 15 screened tree-ring chronologies produced 12 nested discharge reconstructions, each created by sequentially running PCR
on decreasing subsets of chronologies with progressively earlier
starting years. The complete nested reconstruction (Fig. 3) extends
from 1452 to 2004 (2005–08 are appended instrumental data) and
the changing number of chronologies used is shown below it. The
reconstruction includes the 2-tailed 90% semi-parametric prediction intervals for the reconstructed values, as described in the previous section. Below the reconstruction plot are the prediction
intervals calculated two ways. One follows Eq. (1) exactly by using
the parametric t-test to produce the 90% prediction intervals and
the other uses the MEBoot reconstruction 5% and 95% quantiles
as a replacement for the t-test. Only 20-year low-pass values of
each are shown for easy comparison, but they are all based on
annually resolved values. The semi-parametric intervals based on
MEBoot are typically wider, asymmetric, and more data driven
compared to the intervals based on the t-statistic. In this sense,
they more realistically express the uncertainties in the reconstruction and should therefore be preferred.
In terms of the model calibration and validation, the five statistics described earlier – CRSQ, CVRE for calibration and VRSQ, VRE,
and VCE for validation – are listed in Table 1 as directly estimated
from the actual and estimated values and as medians from the 300
nested MEBoot pseudo-reconstructions. Both versions of the statistics are positive for all nests back to 1452, which suggests that the
reconstruction is valid over its entire interval. However, Fig. 4 provides a somewhat different and more complete evaluation of calibration and validation performance once the 90% quantile limits
are added to the changing medians. Except for VRSQ, the lower
90% limits intersect or cross below the zero line before 1480. This
result indicates that the reconstruction should be interpreted with
greater caution before that year. The 90% limits are also highly
assymmetric (negatively skewed) as expected given that the upper
limit of each statistics is bounded by 1.0. In addition, the lower limits expand noticeably towards zero as the number of chronologies
Please cite this article in press as: Cook, E.R., et al. Five centuries of Upper Indus River flow from tree rings. J. Hydrol. (2013), http://dx.doi.org/10.1016/
j.jhydrol.2013.02.004
7
E.R. Cook et al. / Journal of Hydrology xxx (2013) xxx–xxx
Upper Indus Basin May-September Streamflow Reconstruction
5000
4000
3000
20
2000
10
1000
1500
1580
1660
1740
Years
1820
1900
1980
0
Ncrns
Discharge (m3s-1)
6000
Discharge (m3s-1)
6000
T-test 90% Prediction Intervals
5000
MEBoot 90% Prediction Intervals
4000
3000
2000
1500
1580
1660
1740
1820
1900
1980
Years
Fig. 3. Reconstruction of May–September discharge at Partab Bridge on the Upper Indus River Basin since 1452 (top plot). The annual reconstruction (red) with 20-year lowpass filtered smooth (black) are shown with 90% MEBoot uncertainties (gray) as described in the text. The instrumental data since 1962 shown in Fig. 2 is indicated by the
solid blue dots. The long-term mean (3545 m3 s!1) is indicated by the dashed line. It highlights the anomalous high flow period since 1988. The changing number of tree-ring
chronologies used per reconstruction nest are also shown as Ncrns. The bottom plot is a comparison of prediction intervals (Eq. (1)) calculated parametrically using the
standard t-test (blue curves) and semi-parametrically using the maximum entropy bootstrap in place of the t-test (red curves). Only the 20-year low-pass values of each are
shown for easy comparison. The MEBoot intervals are typically wider and asymmetric compared to the intervals based on the t-statistic. (For interpretation of the references
to colour in this figure legend, the reader is referred to the web version of this article.)
Table 1
The complete nested calibration/validation results for the tree-ring reconstruction of May–September discharge at Partab Bridge on the upper Indus River of northern Pakistan.
The starting year of each nest is indicated under IFYR. Note that except for the starting years of the first and last nests, if the starting years of the tree-ring chronologies used in the
intermediate nests fall within a decade interval, their start years are rounded up to the next decade to insure that at least 10 years separated those nests. The number of
chronologies used per nest are indicated under NCRN. The five calibration and validation statistics CRSQ, CVRE, VRSQ, VRE, and VCE are described in the text. Statistic #1 (e.g.,
CRSQ1) in each case is the standard calibration or validation statistic calculated directly from the actual and reconstructed data; statistic #2 (e.g., CRSQ2) is the median value
based on 300 MEBoot pseudo-reconstructions. Calculated either way, the results indicate highly robust calibration and validation statistics. Nests 1–11 have remarkably stable
calibration and validation statistics from nest to nest given the decline in chronologies available. The quality of the earliest nest #12 based on only one chronology is clearly
inferior to the others.
NEST
IFYR
NCRN
CRSQ1
CRSQ2
CVRE1
CVRE2
VRSQ1
VRSQ2
VRE1
VRE2
VCE1
VCE2
1
2
3
4
5
6
7
8
9
10
11
12
1800
1780
1750
1690
1670
1650
1560
1540
1530
1480
1470
1452
15
14
13
12
11
10
8
6
5
4
3
1
0.554
0.476
0.497
0.485
0.525
0.529
0.468
0.427
0.446
0.422
0.357
0.139
0.521
0.488
0.481
0.461
0.496
0.499
0.451
0.410
0.428
0.404
0.329
0.127
0.494
0.395
0.421
0.407
0.455
0.459
0.383
0.330
0.354
0.320
0.240
0.037
0.454
0.414
0.404
0.384
0.425
0.429
0.370
0.316
0.338
0.307
0.221
0.022
0.449
0.589
0.613
0.562
0.552
0.564
0.555
0.625
0.622
0.683
0.612
0.167
0.514
0.569
0.609
0.569
0.559
0.569
0.556
0.624
0.617
0.671
0.579
0.163
0.431
0.495
0.527
0.502
0.523
0.531
0.481
0.548
0.547
0.579
0.517
0.165
0.476
0.527
0.551
0.528
0.546
0.551
0.483
0.577
0.573
0.607
0.524
0.168
0.406
0.473
0.507
0.481
0.503
0.511
0.458
0.528
0.528
0.561
0.496
0.129
0.453
0.509
0.531
0.511
0.525
0.532
0.465
0.560
0.554
0.592
0.508
0.131
used in the nests declines. This is especially evident before 1560
when the number of chronologies available drops below 10. All
of these insights into calibration and validation performance have
been possible through the use of the maximum entropy bootstrap.
Overall, the reconstruction calibration/validation results are
significant and stable for all nests back to 1480. This is a remarkable result given the extreme topographic complexity of the UIB
and the declining number of tree-ring chronologies available for
reconstruction back in time. It clearly refutes the suggestion of Archer and Blenkinsop (2010) that tree rings may not be able to
reconstruct discharge in the UIB because of the topographically
complex nature of the terrain there. A sufficiently dense,
multi-species tree-ring network has overcome those putative barriers to provide a successful streamflow reconstruction.
6. Comparisons with other independent records
As strong as the calibration and validation results just presented
appear to be, they still only provide information on how accurate
the tree-ring estimates of streamflow are over a very restricted
time period. In order to better assess the long-term accuracy and
stability of the reconstruction, we compared it to three independent tree-ring-based records of hydroclimatic variability from the
UIB not used in the reconstruction. These three records cover the
Please cite this article in press as: Cook, E.R., et al. Five centuries of Upper Indus River flow from tree rings. J. Hydrol. (2013), http://dx.doi.org/10.1016/
j.jhydrol.2013.02.004
8
CRSQ
(B) CVRE - Calibration period cross-validation RE
CVRE
1
0.8
0.6
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
(C) VRSQ - Validation period R2
(D) VRE - Validation period RE
VRE
1
0.8
0.6
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
(E) VCE - Validation period CE
Normal Deviate Normal Deviate Normal Deviate Normal Deviate
(A) CRSQ - Calibration period R2
VRSQ
1
0.8
0.6
0.4
0.2
0
VCE
E.R. Cook et al. / Journal of Hydrology xxx (2013) xxx–xxx
2
(A) Indus River Reconstruction
0
-2
2
(B) Treydte Juniper δ18O Record
0
-2
2
(C) Esper High-Elevation Juniper
0
-2
2
(D) Esper Low-Elevation Juniper
0
-2
1440
1520
1600
1680
1760
1840
1920
2000
Year
1500
1600
1700
1800
1900
2000
Year
Fig. 4. Calculated calibration and validation statistics (thick solid line) and their
upper and lower 90% uncertainty quantiles (short dashes) for the calibration and
validation statistics produced from 300 MEBoot pseudo-reconstructions. The
changes in those statistics over time reflect changes in the chronologies used for
each nested reconstruction. See the text for details. If the lower limit crosses the
indicated zero line, the statistic for that nest is not significant at the 90% level.
entire span of the streamflow reconstruction back to 1452 and thus
provide a complete comparison. The first series is an annually resolved oxygen isotope record from tree-ring cellulose of Juniper
trees growing in the high mountains of northern Pakistan (Treydte
et al., 2006). This record provides a millennium-length expression
of winter precipitation variability for the UIB. As such, it indicates
that the 20th century was the wettest period in northern Pakistan
over the last 1000 years (Treydte et al., 2006). The other records are
composites based on 16 northern Pakistan Juniper data sets developed by Esper et al. (1995), Esper et al. (2007), Esper (2000), but
not used for reconstruction here because they all ended in the
1990s. These data have been pooled into high-elevation (11 sites
>3500 m) and low-elevation (5 sites <3500 m) groups following
the guidelines of Esper et al. (2007); their Table 1) and standardized using the ‘signal free’ method (Melvin and Briffa, 2008). Pooling the data this way allowed for a comparison of reconstructed
UIB discharge and tree growth from locations that are inferred to
be more temperature limited at higher elevations and more moisture limited at lower elevations (Esper et al., 2007).
Fig. 5 shows plots of the UIB discharge reconstruction (A), the
Juniper oxygen isotope record (B), and the upper (C) and lower
(D) elevation Juniper chronologies, all transformed into standard
normal deviates for easy comparison. To facilitate this initial qualitative comparison, vertical gray bars have been added that link
certain periods of reasonable visual agreement. Overall, the Esper
high and low Juniper records appear to match the streamflow
reconstruction a bit better than the oxygen isotope record. In order
to quantitatively determine the degree to which this is true, we
Fig. 5. Plots of the UIB discharge reconstruction (A), the Juniper oxygen isotope
record (B), the upper (C) and lower (D) elevation Juniper chronologies; all
transformed into standard normal deviates for easy comparison. Shaded areas
indicate periods thought to contain similar response patterns.
used the Kalman filter as a dynamic regression-modeling tool (Visser and Molenaar, 1988) for the primary test of association. It uses
maximum likelihood estimation to objectively test for the statistical association between reconstructed discharge and in so doing
explicitly evaluate the association for the presence of time dependence. In the process, the Kalman filter also provides theory-based
uncertainties. See Visser and Molenaar (1988) for details and Cook
and Johnson (1989) for another example application.
Fig. 6 shows the Kalman filter results in which the UIB discharge
reconstruction has been dynamically regressed on each of the test
series as described above. In each case, the solid black curve shows
the changing standardized regression coefficients (beta weights)
and the dashed curves above and below are 2-standard error limits. Where the lower limits cross zero the beta weights are no longer considered statistically significant. For comparison to the
Kalman filter results, the overall simple correlation between each
pair of series is also provided. With respect to simple correlation
alone, the three test series are each positively correlated
(p < 0.01) with the UIB discharge reconstruction, but the ringwidth-based Esper series have produced the highest correlations.
The signs of the correlations are also consistent with expectation:
oxygen isotope variation is a direct indicator of winter precipitation and the ring-width chronologies are direct indicators of moisture availability and temperature.
The time-dependent traces of the beta weights tell a much more
complete story. Most of the significant correlation between discharge and oxygen isotopes comes from the outer 200 years of record, with the earlier portion wandering in and out of significance
back to 1452. If the oxygen isotope record was the only series compared to the discharge reconstruction, it would not be possible to
tell which series is the primary cause of the time dependence.
However, the beta weights of the Esper high and low series show
a much more stable association between discharge and Juniper ring
widths, with both being significant over most of their records back
to 1452. The declines in their betas prior to about 1640 could be
Please cite this article in press as: Cook, E.R., et al. Five centuries of Upper Indus River flow from tree rings. J. Hydrol. (2013), http://dx.doi.org/10.1016/
j.jhydrol.2013.02.004
E.R. Cook et al. / Journal of Hydrology xxx (2013) xxx–xxx
Beta Weight
Beta Weight
Beta Weight
Kalman Filter Comparisons of Indus River Reconstruction
to Three Independent UIB Tree-Ring Records
1
(A) Indus River Recon vs. Treydte δO18
Overall R = 0.269
0.5
0
1
(B) Indus River Recon vs. Esper High Juniper
Overall R = 0.420
(C) Indus River Recon vs. Esper Low Juniper
Overall R = 0.469
0.5
0
1
0.5
0
1440
1520
1600
1680
1760
Year
1840
1920
2000
Fig. 6. Kalman filter comparisons of the Indus River reconstruction to three
Juniperus UIB tree-ring records not used in the reconstruction. The Kalman filter is
being used here as a dynamic regression modeling tool, which allows for the
association between variables to change over time in an objectively determined
manner based on maximum likelihood estimation (Visser and Molenaar, 1988). The
solid black traces show how the standardized regression coefficients (beta weights)
of reconstructed Indus River discharge vary when estimated by the each Juniperus
series in this way. The dashed traces are ±2 standard error limits of the beta
weights. Where the lower limits cross zero, the beta weights are not considered
statistically significant at that point in time.
related to the decline in the number of chronologies used for
reconstruction (Table 1). In the case of the Esper low series, the
replication in that chronology also declines rapidly before that
time as well (see Esper et al., 2007; their Fig. 2). Each of these replication issues is probably contributing to the estimated decline in
the betas, but overall the comparisons of reconstructed discharge
with the Esper high and low chronologies indicate significant stability, if not accuracy, in the reconstructed discharge values back
to 1452.
7. Discussion
The May–September streamflow reconstruction at Partab
Bridge has many implications for the long-term runoff properties
of the UIB. The long-term mean discharge estimated from the
reconstruction (including the 2005–2008 instrumental-only data)
is 3545 m3 s!1, which is below the 1962–2008 gauged mean of
3674 m3 s!1 by 3.5%. It is also closer to the mean for the early
1962–1987 period (3470 m3 s!1) than for the late 1988–2008 period (3926 m3 s!1). These differences between actual and reconstructed means are unlikely to be statistically significant when
the prediction interval uncertainties are factored in, but they do
suggest that 1988–2008 Indus River discharge at Partab Bridge
has been unusually high on average over that period nonetheless.
This indication is further supported by the fact that it is necessary
to go back to 1684–1700 (mean: 3904 m3 s!1) to find a comparable
high-flow period like that seen since 1988. The reconstruction also
highlights the fact that interdecadal variability on the scale seen in
the observed discharge record has been a common feature of Indus
river discharge since 1452. In fact, the power spectrum of the
reconstruction (not shown) has a quasi-periodic peak centered
on 27 years that exceeds the 99% significance level from a red noise
null continuum background. Therefore, the earlier proposed null
hypothesis for natural interdecadal variability being the most
9
likely cause of the apparent regime shift in discharge from 1987
to 1988 cannot be rejected based on the pronounced interdecadal
variability in the reconstruction since 1452.
With this in mind, the long-term reconstructed mean
(3545 m3 s!1) should be used as the best estimate of expected
May–September discharge at Partab Bridge in the future, but the
continuation of strong interdecadal variability in the future, like
that found in the past, would most likely cause multi-year departures from this expectation to occur. This statement assumes that
climatic change over the UIB in the future will neither disrupt
the continuation of interdecadal variability found in the past nor
meaningfully increase the glacier melt water discharge component. To date, the latter does not appear to be happening if the current stable state of the Karakoram glaciers is any indication
(Hewitt, 2005; Armstrong, 2010; Gardelle et al., 2012).
Perhaps the most worrying feature in the streamflow reconstruction is the occurrence of a pronounced and prolonged
112 year low-flow period from 1572 to 1683 (mean:
3377 m3 s!1) and a shorter but drier 27 year period from 1637 to
1663 (mean: 3271 m3 s!1). The former is 8.1% below and the latter
11% below the overall mean of the observed discharge record at
Partab Bridge (3674 m3 s!1). Should either of these low-flow periods repeat in the future, the resulting cumulative deficit could seriously reduce Pakistan’s capacity for irrigation and hydroelectric
power generation provided by the Tarbela Reservoir and Dam.
Whether or not the anomalous high flow period since 1988 is
from increases in seasonal snow melt or glacier melt cannot be answered definitively at this time, but the weight of the evidence
leans towards the former. As discussed earlier, Karakoram glaciers
are not retreating in any consistent way and in some cases are
actually advancing or surging (Hewitt, 2005; Armstrong, 2010;
Gardelle et al., 2012). In addition, summer temperatures over the
UIB have recently decreased (Fowler and Archer, 2006; Shekhar
et al., 2010), which would slow glacier melting. There is also evidence for an increase in winter and summer precipitation from
1961 to 1999 over the UIB (Archer and Fowler, 2004), which would
add to summer runoff. So it is doubtful that increased glacier meltwater is the primary cause of the recent flow increase since 1988.
8. Conclusions
The May–September discharge reconstruction presented here is
a significant contribution to our understanding of the long-term
streamflow dynamics of Upper Indus River, which is primarily controlled by meltwater contributions from seasonal snowfall and glaciers. It is a well-calibrated and validated reconstruction, both by
comparison to the short instrumental record and back to 1452
when compared to independent tree-ring records of past hydroclimatic variability from the same UIB region. The indicated presence
of strong inter-decadal fluctuations in the reconstruction has
emerged now as a common mode of hydroclimatic variability
there, which could not have been deduced with any confidence
from the short gauge record at Partab Bridge since 1962. This discovery further illustrates how short discharge records can severely
limit our ability to statistically model hydrologic variability (Rodriguez-Iturbe, 1969). As such, the reconstruction helps fill the hydrological ‘‘data gap’’ for modeling the northern Pakistan part of the
Hindu Kush–Karakoram–Himalayan region (Pellicciotti et al.,
2012), and it should be useful to better plan for the future development of UIB water resources in an effort to close Pakistan’s ‘‘water
gap’’ (World Bank, 2005). Finally, the May–September discharge
reconstruction provides the basis for comparing past, present,
and future hydrologic changes, which will be crucial for detection
and attribution of future hydroclimate change in the Upper Indus
River Basin. At present, it appears that an observed persistant
Please cite this article in press as: Cook, E.R., et al. Five centuries of Upper Indus River flow from tree rings. J. Hydrol. (2013), http://dx.doi.org/10.1016/
j.jhydrol.2013.02.004
10
E.R. Cook et al. / Journal of Hydrology xxx (2013) xxx–xxx
increase in UIB discharge from 1988 to 2008 is not statistically
unprecedented and is more likely to be associated with increased
meltwater from heavier prior winter snow accumulation than from
enhanced summer glacier melting.
Acknowledgements
We gratefully acknowledge the help of the Pakistan Water and
Power Development Authority (WAPDA), Higher Education Commission (HEC) of Pakistan, and the Pakistan Meteorological Department (PMD) in conducting our research in Pakistan. We also thank
Jan Esper and Kirstin Treydte for the long Juniperus records used
for comparison. Four anonymous reviewers also provided excellent
suggestions that improved the paper. The authors were supported
by the U.S. Agency for International Development (USAID) through
NAS Grant PGA-P280423 and EC later by the U.S. Department of
Energy Grant DE-SC0006616 LDE. Lamont-Doherty Earth Observatory Contribution Number 7668.
References
Ahmed, M., 1989. Tree-ring chronologies of Abies pindrow (Royle) Spach, from the
Himalayan region of Pakistan. Pak. J. Bot. 21 (2), 347–354.
Ahmed, S., Joyia, M.F., 2003. NASSD Background Paper: Water. IUCN Pakistan,
Northern Areas Progamme, Gilgit. 67 pp.
Ahmed, M., Naqvi, S.H., 2005. Tree-ring chronologies of Picea smithiana (Wall) Boiss.
and its quantitative vegetational description from Himalayan range of Pakistan.
Pak. J. Bot. 37, 697–707.
Ahmed, M., Sarangezai, A.T., 1991. Dendrochronological approach to estimate age
and growth rate of various species from Himalayan region of Pakistan. Pak. J.
Bot. 23, 78–89.
Ahmed, M., Palmer, J., Khan, N., Wahab, M., Fenwick, P., Esper, J., Cook, E., 2011. The
dendroclimatic
potential
of
conifers
from
northern
Pakistan.
Dendrochronologia 29, 77–88.
Alford, D., 2011. Hydrology and glaciers in the Upper Indus Basin, South Asia
Sustainable Development (SASDN). South Asia Agriculture and Rural
Development Unit, The World Bank, Washington, DC.
Ammann, C.M., Genton, M.G., Li, B., 2010. Technical note: correcting for signal
attenuation from noisy proxy data in climate reconstructions. Clim. Past 6 (2),
273–279.
Archer, D., 2003. Contrasting hydrological regimes in the Upper Indus Basin. J.
Hydrol. 274, 198–210.
Archer, D., Blenkinsop, S., 2010. Heterogeneity and spatial representativeness of
station climate and tree-ring records as climate change indicators in the Upper
Indus Basin. In: Talk presented at International Conference/Workshop on
Dendrochronology held at Federal Urdu University, Karachi, November 15,
2010.
Archer, D., Fowler, H.J., 2004. Spatial and temporal variations in precipitation in the
Upper Indus Basin, global teleconnections and hydrological implications.
Hydrol. Earth Syst. Sci. 8 (1), 47–61.
Armstrong, R., 2010. The glaciers of the Hindu Kush–Himalayan Region: a summary
of the science regarding glacier melt/retreat in the Himalayan, Hindu Kush,
Karakoram, Pamir, and Tien Shan mountain ranges. ICIMOD, Kathmandu, 20pp.
Bolch, T., Kulkarni, A., Kääb, A., Huggel, C., Paul, F., Cogley, J.G., Frey, H., Kargel, J.S.,
Fujita, K., Scheel, M., Bajracharya, S., Stoffel, M., 2012. The state and fate of
Himalayan glaciers. Science 336 (6079), 310–314.
Bookhagen, B., Burbank, D.W., 2010. Toward a complete Himalayan hydrological
budget: spatiotemporal distribution of snowmelt and rainfall and their impact
on river discharge. Journal of Geophysical Research. vol. 115. (F03019) doi:
10.1029/2009JF001426.
Chow, V.T., Maidment, D.R., Mays, L.W., 1988. Applied Hydrology. McGraw Hill Book
Company, ISBN 0-07-010810-2. 572pp.
Cleaveland, M.K., 1999. A 963-year reconstruction of summer (JJA) streamflow in
the White River, Arkansas, USA, from tree-rings. The Holocene 10, 33–41.
Cook, E.R., Jacoby, G.J., 1983. Potomac River streamflow since 1730 as reconstructed
by tree rings. J. Climate Appl. Meteorol. 22, 1659–1672.
Cook, E.R., Johnson, A.H., 1989. Climate change and forest decline: a review of the
red spruce case. Water Air Soil Pollut. 48, 127–140.
Cook, E.R., Kairiukstis, L., 1990. Methods of Dendrochronology. Kluwer, Dordrecht,
406pp.
Cook, E.R., Peters, K., 1981. The smoothing spline: a new approach to standardizing
forest interior tree-ring width series for dendroclimatic studies. Tree-Ring Bull.
41, 45–53.
Cook, E.R., Briffa, K.R., Meko, D.M., Graybill, D.S., Funkhouser, G., 1995. The ‘segment
length curse’ in long tree-ring chronology development for paleoclimatic
studies. Holocene 5, 229–237.
Cook, E.R., Meko, D.M., Stahle, D.W., Cleaveland, M.K., 1999. Drought
reconstructions for the continental United States. J. Clim. 12, 1145–1162.
Cook, E.R., D’Arrigo, R.D., Mann, M.E., 2002. A well-verified, multiproxy
reconstruction of the winter North Atlantic oscillation index since AD 1400. J.
Clim. 15, 1754–1764.
Cook, E.R., Woodhouse, C., Eakin, C.M., Meko, D.M., Stahle, D.W., 2004.
Long-term aridity changes in the western United States. Science 306, 1015–
1018.
Cook, E.R., Anchukaitis, K.J., Buckley, B.M., D’Arrigo, R.D., Jacoby, G.C., Wright, W.E.,
2010a. Asian monsoon failure and megadrought during the last millennium.
Science 328 (5977), 486–489.
Cook, E.R., Seager, R., Heim, R.R., Vose, R.S., Herweijer, C., Woodhouse, C.W., 2010b.
Megadroughts in North America: placing IPCC projections of hydroclimatic
change in a long-term paleoclimate context. J. Quat. Sci. 25 (1), 48–61.
Crutzen, P.J., 2002. Geology of mankind. Nature 415, 23.
Efron, B., 1979. Bootstrap methods: another look at the jackknife. Ann. Stat. 7, 1–26.
Esper, J., 2000. Long term tree-ring variations in junipers at the upper timberline in
the Karakorum (Pakistan). The Holocene 10, 253–260.
Esper, J., Bosshard, A., Schweingruber, F.H., Winiger, M., 1995. Tree-rings from the
upper timberline in the Karakorum as climatic indicators for the last
1000 years. Dendrochronologia 13, 79–88.
Esper, J., Frank, D.C., Wilson, R.J.S., Buentgen, U., Treydte, K., 2007. Uniform growth
trends among central Asian low- and high-elevation juniper tree sites. Trees 21,
141–150.
Fowler, H.J., Archer, D.R., 2006. Conflicting signals of climate change in the Upper
Indus Basin. J. Clim. 19 (17), 4276–4293.
Fritts, H.C., 1976. Tree Rings and Climate. Academic Press, New York, 567pp.
Gardelle, J., Berthier, E., Arnaud, Y., 2012. Slight mass gain of Karakoram glaciers in
the early 21st century. Nat. Geosci. 5, 322–325.
Gove, J.M., 1988. The Little Ice Age. Methuen, London and New York, 498 pp.
Hegerl, G.C., Crowley, T.J., Allen, M., Hyde, W.T., Pollack, H.N., Smerdon, J., Zorita, E.,
2007. Detection of human influence on a new, validated 1500-year temperature
reconstruction. J. Clim. 20, 650–666.
Hewitt, K., 2005. The Karakoram anomaly? Glacier expansion and the ‘elevation
effect’, Karakoram, Himalaya. Mount. Res. Develop. 25 (4), 332–340.
ICIMOD, 2010. Islamic Republic of Pakistan: Glacial Melt and Downstream Impacts
on Indus Dependent Water Resources and Energy. Technical Assistance
Consultant’s Report for the Asian Development Bank, Project Number
RETA6420. 50pp.
Immerzeel, W.W., Droogers, P., de Jong, S.M., Bierkens, M.F.P., 2009. Large-scale
monitoring of snow cover and runoff simulation in Himalayan river basins
using remote sensing. Remote Sens. Environ. 113, 40–49.
Immerzeel, W.W., van Beek, L.P.H., Bierkens, M.F.P., 2010. Climate change will affect
the Asian water towers. Science 328, 1382–1385.
Meko, D.M., 1997. Dendroclimatic reconstruction with time varying subsets of tree
indices. J. Clim. 10, 687–696.
Meko, D., Woodhouse, C.A., Baisan, C.A., Knight, T., Lukas, J.J., Hughes, M.K., Salzer,
M.W., 2007. Medieval drought in the upper Colorado River Basin. Geophys. Res.
Lett. 34 (L10705) doi: 10.1029/2007GL029988.
Melvin, T.M., Briffa, K.R., 2008. A ‘‘signal-free’’ approach to dendroclimatic
standardisation. Dendrochronologia 26 (2), 71–86.
Michaelsen, J., 1987. Cross validation in statistical climate forecast models. J.
Climate Appl. Meteorol. 26, 1589–1600.
Olive, D.J., 2007. Prediction intervals for regression models. Comput. Stat. Data Anal.
51, 3115–3122.
Pellicciotti, F., Buergi, C., Immerzeel, W.W., Konz, M., Shrestha, A.B., 2012.
Challenges and uncertainties in hydrological modeling of remote Hindu
Kush–Karakoram–Himalayan (HKH) basins: suggestions for calibration
strategies. Mount. Res. Develop. 32 (1), 39–50.
Picard, R.R., Berk, K.N., 1990. Data splitting. Am. Stat. 44 (2), 140–147.
Qureshi, A.S., 2011. Water management in the Indus Basin in Pakistan: challenges
and opportunities. Mount. Res. Develop. 31 (3), 252–260.
Rango, A., Salomonson, V.V., Foster, J.L., 1977. Seasonal streamflow estimation in the
Himalayan region employing meteorological satellite snow cover observations.
Water
Resour.
Res.
13
(1),
109–112.
http://dx.doi.org/10.1029/
WR013i001p00109.
Rodriguez-Iturbe, I., 1969. Estimation of statistical parameters for annual river
flows. Water Resour. Res. 5 (6), 1418–1421.
Schmidt, S., Nusser, M., 2009. Fluctuations of Raikot Glacier during the past
70 years: a case study from the Nanga Parbat massif, northern Pakistan. J.
Glaciol. 55 (194), 949–959.
Seber, G.A.F., Lee, A.J., 2003. Linear Regression Analysis, second ed. Wiley, New
York, 557pp.
Sharif, M., Archer, D.R., Fowler, H.J., Forsythe, N., 2012. Trends in timing and
magnitude of flow in the Upper Indus Basin. Hydrol. Earth Syst. Sci. Discuss. 9,
9931–9966.
Shekhar, M.S., Chand, H., Kumar, S., Srinivasan, K., Ganju, A., 2010. Climate change
studies in the western Himalaya. Ann. Glaciol. 51 (54), 105–112.
Snee, R.D., 1977. Validation of regression models: methods and examples.
Technometrics 19, 415–428.
Stockton, C.W., Jacoby, G.C., 1976. Long-term surface-water supply and streamflow
trends in the Upper Colorado River Basin. Lake Powell Research Project Bulletin
18, National Science Foundation, Arlington, Va. 70pp.
Stokes, M.A., Smiley, T.L., 1968. An Introduction to tree-ring dating. The University
of Chicago Press, Chicago, 73pp.
Treydte, K.S., Schleser, G.H., Helle, G., Frank, D.C., Winiger, M., Haug, G.H., Esper, J.,
2006. The 20th century was the wettest period in northern Pakistan over the
past millennium. Nature 440, 1179–1182.
Please cite this article in press as: Cook, E.R., et al. Five centuries of Upper Indus River flow from tree rings. J. Hydrol. (2013), http://dx.doi.org/10.1016/
j.jhydrol.2013.02.004
E.R. Cook et al. / Journal of Hydrology xxx (2013) xxx–xxx
Vinod, H.D., 2006. Maximum entropy ensembles for time series inference in
economics. J. Asian Econom. 17 (6), 955–978.
Vinod, H.D., 2010. A New Solution to Time Series Inference in Spurious Regression
Problems. Discussion Paper No: 2010-01, Department of Economics, Fordham
University, NY. 37 pp.
Vinod, H.D., López-de-Lacalle, J., 2009. Maximum entropy bootstrap for time series:
the meboot R package. J. Stat. Softw. 29 (5), 1–19.
Visser, H., Molenaar, J., 1988. Kalman filter analysis in dendroclimatology.
Biometrics 44, 929–940.
Weisberg, S., 2005. Applied Linear Regression, third ed. John Wiley, New Jersey,
310pp.
Wilks, D.S., 1997. Resampling hypothesis tests for autocorrelated fields. J. Clim. 11,
65–82.
11
Wilson, R., Wiles, G., D’Arrigo, R., Zweck, C., 2007. Cycles and shifts: 1300-years of
multi-decadal temperature variability in the Gulf of Alaska. Climate Dyn. 28,
425–440.
Winiger, M., Gumpert, M., Yamout, H., 2005. Karakorum–Hindukush–western
Himalaya: assessing high-altitude water resources. Hydrol. Process. 19 (12),
2329–2338.
Woodhouse, C.A., Gray, S.T., Meko, D.M., 2006. Updated streamflow reconstructions
for the Upper Colorado River Basin, Water Resour. Res. 42 (W05415). doi:
10.1029/2005WR004455.
World Bank, 2005. Pakistan Country Water Resources Assistance Strategy. Water
Economy: Running Dry. Report no. 34081-PK, South Asia Region. 145pp.
Please cite this article in press as: Cook, E.R., et al. Five centuries of Upper Indus River flow from tree rings. J. Hydrol. (2013), http://dx.doi.org/10.1016/
j.jhydrol.2013.02.004